J. P. Cohoon and J. W. Davidson© 1999 McGraw-Hill, Inc.

Programmer-defined functions

Development of simple functions using value parameters

Ch 6 / Foil 2

Includes description of the interface and the function body Interface

– Similar to a function prototype, but parameters names are required

Body– Statement list with curly braces that comprises its actions– Return statement to indicate value of invocation

Function Definition

Ch 6 / Foil 3

float CircleArea (float r) {const float Pi = 3.1415;return Pi * r * r;

}

Function Definition

Function bodyReturn statement

Local object definition

Formal parameterReturn type Function name

Ch 6 / Foil 4

Function Invocation

cout << CircleArea(MyRadius) << endl;

Invocation is part of a larger expression. To process the invocation, the function that

contains the insertion statement is suspended and CircleArea() does its job.

The insertion statement is then completed using the value supplied by CircleArea().

Actual parameter

Ch 6 / Foil 5

Simple Programs

Single file Include statements Using statements Function prototypes Function definitions

Functions use value parameter passing Also known as pass by value or call by value

– The actual parameter is evaluated and a copy is given to the invoked function

Ch 6/ Foil 6

#include <iostream>#include <string>using namespace std;float CircleArea(float r);// main(): manage circle computationint main() { cout << "Enter radius: "; float MyRadius; cin >> MyRadius; float Area = CircleArea(MyRadius); cout << "Circle has area " << Area; return 0;}// CircleArea(): compute area of radius r circlefloat CircleArea(float r) { const float Pi = 3.1415; return Pi * r * r;

}

Ch 6 / Foil 7

Value Parameter Passing Rules

Formal parameter is created on function invocation and it is initialized with the value of the actual parameter

Changes to the formal parameter do not affect the actual parameter Whenever a formal parameter is referenced, the value used for the

formal parameter is the one stored in the current activation record for the function

There is a new activation record for each invocation The name of the formal parameter is only known within its function The formal parameter is destroyed when the function invocation

completes Activation record memory is automatically released at completion

Returnvalue

FunctionInput stream

data

Output streamdata

Information to function cancome from parameters or

an input stream

Parameters

Information fromfunction can come

through a returnvalue or an output

stream

Ch 6/ Foil 8

Ch 6 / Foil 9

PromptAndRead()

// PromptAndRead(): prompt and extract next// integerint PromptAndRead() {

cout << "Enter number (integer): ";int Response;cin >> Response;return Response;

}

Ch 6 / Foil 10

Max()

// Max(): return larger of a and bint Max(int a, int b) {

if (a < b) {return b;

}else {

return a;}

}

Ch 6 / Foil 11

Min()

// Min(): return smaller of a and bint Min(int a, int b) {

if (a > b) {return b;

}else {

return a;}

}

Ch 6 / Foil 12

Sum()

// Sum(): compute sum of integers in a ... bint Sum(int a, int b) {

int Total = 0;for (int i = a; i <= b; ++i) {

Total += i;}return Total;

}

Ch 6 / Foil 13

Problem

Definition Input two numbers that represent a range of integers and

display the sum of the integers that lie in that range Design

Prompt user and read the first number Prompt user and read the second number Determine the smaller of the two numbers Determine the larger of the two numbers Calculate the sum of integers in the range smaller...larger by

adding in turn each integer in that range Display the sum

#include <iostream>#include <string>using namespace std;int PromptAndRead();int Min(int a, int b);int Max(int a, int b);int Sum(int a, int b);int main() {

int FirstNumber = PromptAndRead();int SecondNumber = PromptAndRead();int Smaller = Min(FirstNumber, SecondNumber);int Larger = Max(FirstNumber, SecondNumber);int RangeSum = Sum(Smaller, Larger);cout << "The sum from " << Smaller << " to " << Larger << " is " << RangeSum << endl;return 0;

}

Ch 6/ Foil 14

// Min(): return smaller of a and bint Min(int a, int b) {

if (a > b)return b;

elsereturn a;

}// Max(): return larger of a and bint Max(int a, int b) {

if (a < b)return b;

elsereturn a;

}

Ch 6/ Foil 15

// PromptAndRead(): prompt & extract next integerint PromptAndRead() {

cout << "Enter number (integer): ";int Response;cin >> Response;return Response;

}// Sum(): compute sum of integers in a ... bint Sum(int a, int b) {

int Total = 0;for (int i = a; i <= b; ++i) {

Total += i;}return Total;

}

Ch 6/ Foil 16

Ch 6 / Foil 17

Blocks and Local Scope

A block is a list of statements within curly braces Blocks can be put anywhere a statement can be put Blocks within blocks are nested blocks An object name is known only within the block in which it is

defined and in nested blocks of that block A parameter can be considered to be defined at the beginning of

the block corresponding to the function body

Ch 6 / Foil 18

Local Object Manipulation

void f() { int i = 1; cout << i << endl; // insert 1 { int j = 10;

cout << i << j << endl; // insert 1 10 i = 2; cout << i << j << endl // insert 2 10 } cout << i << endl; // insert 2 cout << j << endl; // illegal}

Ch 6 / Foil 19

Name Reuse

If a nested block defines an object with the same name as enclosing block, the new definition is in effect in the nested block

void f() { { int i = 1; cout << i << endl; // insert 1 { cout << i << endl; // insert 1 char i = 'a'; cout << i << endl; // insert a } cout << i << endl; // insert 1 } cout << i << endl; // illegal insert}

Ch 6/ Foil 20

Ch 6 / Foil 21

Global Scope

Objects that are not defined within a block are global objects A global object can be used by any function in the file that is

defined after the global object It is best to avoid programmer-defined global objects

Exceptions tend to be important constants Global objects with appropriate declarations can even be used in

other program files cout, cin, and cerr are global objects that are defined in

by the iostream library Local objects can reuse a global object's name Unary scope operator :: can provide access to global object even

if name reuse has occurred

Ch 6 / Foil 22

Example

int i = 1;int main f() { cout << i << endl; // insert 1 char i = 'a'; cout << i << endl; // insert a ::i = 2; cout << i << endl; // insert a cout << ::i << endl; // insert 2 return 0;}

Ch 6 / Foil 23

Integrating Quadratic Polynomials

A polynomial f(x) of degree n is a function whose value is the sum of n+1 terms where the terms are of the form aixi, 0 i n, with the restriction that an is not 0.

anxn + an–1xn–1 + … + a2x2 + a1x + a0

The area under the curve along the x-axis interval (s, t) for f(x) is

an ( sn +1 - tn+1) + an–1 ( sn - tn) + … + a1 (t2 - s2)/2 + a0 (t - s)

For a quadratic polynomial (degree 2) this equation reduces

a2(t3 - s3)/3 + a1(t2 - s2)/2 +a0(t - s)

Ch 6 / Foil 24

QuadraticArea()

double QuadraticArea(double a2, double a1, double a0, double s, double t) {

double term2 = a2*(t*t*t - s*s*s)/3.0;double term1 = a1*(t*t - s*s)/2.0;double term0 = a0*(t - s);return term2 + term1 + term0;

}

#include <iostream> // program 6.3#include <string>using namespace std; double QuadraticArea(double a2, double a1, double a0, double s, double t);int main() {

cout << "Enter quadratic coefficients (n n n): ";double a2, a1, a0;cin >> a2 >> a1 >> a0;cout << "Enter interval of interest (n n): ";double s, t;cin >> s >> t;double Area = QuadraticArea(a2, a1, a0, s, t);cout << "The area of quadratic polynomial " << a2 << "x*x + " << a1 << "x + " << a0 << " for (" << s << ", " << t << ")" << " is " << QuadraticArea(a2, a1, a0, s, t) <<

endl;}

Ch 6 / Foil 26

Recursion

Recursion is the ability of a function to call itself. Consider the mathematical function n!

n! = n * (n-1) … * 2 * 1

is not mathematically precise because we use an ellipsis (…). Consider the following formal definition

n! = 0, if n = 0 n! = n * (n-1)!, if n > 0

– The factorial function is defined in terms of itself

Ch 6 / Foil 27

Consider

#include <iostream>#include <string>using namespace std;int main() {

cout << "Enter a positive integer: ";int n;cin >> n;cout << n << "! = " << Factorial(n) << endl;return 0;

}

Ch 6 / Foil 28

Using

int Factorial(int n) {if (n == 0) {return 1;

}else {return n * Factorial(n-1);

}} C++ function mirrors the mathematical factorial definition

If the value of n is 0, the value 1 is returned. Otherwise, the product of n and Factorial(n-1) is returned.

Ch 6 / Foil 29

Recursion Visualization

Consider cout << n ! = " << Factorial(3) << endl;

cout << "n! = " << Factorial(3) << endl;

n = 3

n = 2

n = 1

n = 0

Factorial(3) = 3 * Factorial(2) = 3 * 2 = 6

Factorial(2) = 2 * Factorial(1) = 2 * 1 = 2

Factorial(1) = 1 * Factorial(0) = 1 * 1 = 1

Factorial(0) = 1

Activation records

call Factorial(0) return 1

call Factorial(1)

call Factorial(2)

call Factorial(3)

return 1

return 2

return 6